2. Fannie Mae and Freddie Mac allow home buyers to get below-market-rate mortgages. They blew up in the housing bust, requiring a massive federal bailout.

We haven't talked so much about a third example of a federal housing subsidy that doesn't seem like a subsidy: the Federal Housing Administration, aka FHA.

Like Fannie and Freddie before the housing crisis, FHA has always funded itself. And, like Fannie and Freddie after the crisis, FHA may soon need a taxpayer bailout. An audit of FHA released today found that the agency is $16 billion in the hole.

The FHA doesn't actually make loans. It guarantees them. If you get an FHA-backed mortgage and don't pay it back, the FHA has to make up the difference. The FHA requires everyone who gets an FHA loan to buy insurance, which is supposed to cover losses when borrowers default.

But the system only works if the FHA prices the insurance correctly. And it appears that, during the early part of the housing bust, the FHA did not collect enough in premiums to pay off losses it will incur in the coming years.

The trouble is likely to come from loans made in 2008 and 2009. At that time, it became increasingly difficult to get a private loan. So more and more borrowers turned to FHA-backed loans, and the agency wound up backing hundreds of billions of dollars in mortgages.

On top of that, FHA loans require only a tiny down payment — as little as 3.5 percent. As a result, when housing prices decline, borrowers very quickly end up owing more than their home is worth. This dramatically raises the risk of default.

The agency has been raising the premiums it charges, among other steps, to try to fix the problem. But today's audit suggests that those steps haven't plugged the hole. FHA will probably need taxpayer money to make good on the promises it made as the housing market was collapsing.

Update: FHA today announced several new steps it's taking to try to plug the hole in its finances. Details here.